5th Workshop on Nuclear Level Density and Gamma Strength. Oslo, May 18-22, Nuclear microscopic strength functions in astrophysical applications

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1 5th Workshop on Nuclear Level Density and Gamma Strength Oslo, May 18-22, 2015 Nuclear microscopic strength functions in astrophysical applications N. Tsoneva Institut für Theoretische Physik, Universität Giessen Sponsored by BMBF project 05P12RGFTE

2 Horst Lenske ww w.ll nl.g ov W. Tornow, A.P. Tonchev, G. Rusev, Krishichayan A. Zilges, V. Derya, M. Spieker, S. Pickstone R. Schwengner P. von Neumann-Cosel Institute of Astronomy and Astrophysics (IAA) Université libre de Bruxelles, Belgium F. Giacoppo, S. Siem, A.C. Larsen, M. Guttormsen S. Goriely

3 NUCLEOSYNTHESIS OF HEAVIER ELEMENTS Heavier elements ( Z> 26-28) can be assembled within stars by neutron capture processes. p-process? r-process Two main neutron capture processes s- process slow neutron capture, low neutron densities ρ ~ 10 8 /cm 3 life time τ ~ 1 10 years s-process r process - rapid neutron captures ρ ~ /cm 3 other processes Fusion in stars

4 Characteristic Response of an Atomic Nucleus to EM Radiation Scissors mode Two-phonon excitation Pygmy-quadrupole resonance Pygmy-dipole resonance Giant M1 resonance Spin-flip M1 Giant Dipole Resonance E1 (GDR) E (MeV) Theoretical prediction of Pygmy Quadrupole Resonance: N. Tsoneva, H. Lenske, Phys. Lett. B 695 (2011) 174. N.Tsoneva, LANZHOU14

5 THE THEORETICAL MODEL Quasiparticle-Phonon Model: V. G. Soloviev: Theory of Atomic Nuclei: Quasiparticles and Phonons (Bristol, 1992) N. Tsoneva, H. Lenske, Ch. Stoyanov, Phys. Lett. B 586 (2004) 213 N. Tsoneva, H. Lenske, Phys. Rev. C 77 (2008) H = + H MF H res Nuclear Ground State ph ph pp HMF = Hsp + H pair H = H + H + H Single-Particle States Phenomenological density functional approach based on a fully microscopic self-consistent Skyrme Hartree-Fock-Bogoljubov (HFB) theory Pairing and Quasiparticle States res M SM M Excited states deformations, vibrations, rotations H M ph - multipole interaction in the particle-hole channel; H SM ph - spin-multipole interaction in the particle-hole channel; H M pp - multipole interaction in the particle-particle channel r r µ λ V( ') ( ) R ( r, r') Y ( θϕ, ) Y ( θ', ϕ') λµτ τ λµ λ µ λ λ R (, r r') = κ R () r R (') r τ τ τ τ λ λ = 0 = 1 isoscalar interaction isovector interaction

6 Phenomenological Density Functional Approach for Nuclear Ground States P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864; W. Kohn, L. J. Sham, Phys. Rev. 140 (1965) A N. Tsoneva, H. Lenske, PRC 77 (2008) The total binding energy B(A) is expressed as an integral over an energy-density functional 1 BA dr U E k pair ( ) ( ) 3 ( ) = q + q q( ) + q, q= p, n 2 effective potential τ ρ ρ ρ ρ δba δρ ρ U ρ U ρ ( r) ( )/ q Σ q( ) = q( ) + q ( ) ρ q, τ q, k q number, kinetic and pairing density neutron skin thickness 1 r r = d rr A q ρ ( ) q q

7 The thickness of the neutron skin scaled with the difference of the Fermi levels of the protons and neutrons Δε F corrected for the Coulomb barrier. Even-Even Neutron-Rich Nucleus E E E c V c (r)~ze 2 /r 132 Sn 0 0 r 124 Sn ε F n 116 Sn Δε F ε F p 108 Sn 104 Sn Neutrons Protons S 2p, S 2n two proton (neutron) separation energies, E C the height of the Coulomb barrier at the nuclear radius (CCF=Coulomb Corrected Fermi energy) a measure of how loosely the neutrons are bound compared to the protons.

8 Calculations of Ground State Densities in Z=50, N=50,82 Nuclei 1 ρ r v j R r q 2 2 () = (2 1) () 2 αq α + q αq 4π r α q Radius [fm] N. Tsoneva, H. Lenske, Phys. Rev. C 77 (2008) R. Schwengner et al., Phys. Rev. C 78 (2008)

9 THEORY OF NUCLEAR EXCITATIONS Quasiparticle-Phonon Model: V. G. Soloviev: Theory of Atomic Nuclei: Quasiparticles and Phonons (Bristol, 1992) The QPM basis is built of phonons: Qλµ i = j j Aλµ j j j j Aλ µ j j 2 λi λ µ λi ψ ( 1 2 1, 2) ( 1) ϕ ( 1 2 1, 2) jj λµ ( 1, 2) = λµ α jmα j m mm A j j jm j m 1 2 A ( j, j ) = jm j m λ µ mm 1 2 i labels the number of the QRPA state The phonons are not pure bosons: Pauli principle + Qλµ i, Qλ ' µ ' i' = δλλ ' δµµ ' δii' + fermionic corrections + QRPA equations are solved: HQ = E Q + +, λµ i λµ i λµ i ~ λ µ α α α jm α j m jm jm

10 ANHARMONICITIES IN NUCLEAR WAVE FUNCTION For even-even nucleus the QPM wave functions are a mixture of one-, two- and three-phonon components one-phonon part two-phonon part three-phonon part M. Grinberg, Ch. Stoyanov, Nucl. Phys. A. 573 (1994) 231

11 NUCLEAR SPECTROSCOPY Μ ( Eλ) = Ψ T( Eλ) Ψ f i T(Eλ) = T Ph (Eλ) + T QPh (Eλ) QRPA + ~ Q λµ QPM ~ α + jm α j ' m ' B(Eλ, J i π i J f π f ) ~ M(Eλ) 2 reduced electric transition probability GDR V. Ponomarev, Ch.Stoyanov, N. Tsoneva, M. Grinberg, Nucl. Phys. A 635 (1998) 470

12 TWO-PHONON 1 - STATES U. Kneissl, N. Pietralla, and A. Zilges, J. Phys. G: Nucl.Part.Phys. 32, R217 (2006) N. Tsoneva, H. Lenske, Ch. Stoyanov, Phys. Lett. B 586 (2004) 213 stable and unstable Sn nuclei Excitation probability of the state from the ground state Excitation probability of the state from the ground state Excitation probability of the state from the ground state E1 transition probability of the state to the state N.Tsoneva, LANZHOU14

13 Systematic studies of two-phonon states in N=82 isotones 95%(2 3 ) %(3 ) QRPA 76%(0 ) 9.2%(3 3 ) QRPA %(31 ) QRPA V. Derya, private communications

14 Parity Measurements with Polarized Photon Beams of Low-energy Dipole Excitations at HIγS, Duke University σ γγ (M1)/σ γγ (E1) ~ 3% 138 Ba A. Tonchev et al., Phys. Rev. Lett. 104, (2010) First systematic spin and parity measurements in comparison with QPM calculations: 138 Ba verified for the first time that the pygmy dipole resonance is predominantly electric dipole in nature. The fine structure of the M1 spin-flip mode is explained. Separation of the PDR to isoscalar and isovector. Interplay between the GDR and the PDR at higher energies.

15 Fine Structure of the Giant M1 Resonance in 90 Zr Precision data on M1 strength distributions are of fundamental importance Spin and Parity Determination at HIγS, Duke University, USA g s eff =0.8 gs bare G. Rusev, N. Tsoneva, F. Dönau, S. Frauendorf, R. Schwengner, A. P. Tonchev, A. S. Adekola, S. L. Hammond, J. H. Kelley, E. Kwan, H. Lenske, W. Tornow, and A. Wagner, Phys. Rev. Lett. 110, (2013). Explaining the fragmentation pattern and the dynamics of the quenching. Multi-particle multi-hole effects increase strongly the orbital part of the magnetic moment. Prediction of M1 strength at and above the neutron threshold. ΣB(M1) Exp. = 4.5 (6) µ N 2 ΣB(M1) QPM. = 4.6 µ N 2 E c.m. Exp. = 9.0 MeV Ec.m. QPM = 9.1 MeV

16 Polarized photon scattering off 52 Cr: Determining the parity of J=1 states. Krishichayan et al., PRC 91, (2015) PDR: TRK sum rule ~ 0.1% = fm cumulative E1 strength cumulative M1 strength

17 LOW-ENERGY ELECTRIC DIPOLE RESPONSE IN 120 Sn extracted from proton inelastic scattering experiments 120 Sn(p,p ): A.M.Krumbholz, P.von Neumann-Cosel, T.Hashimoto, et al.,plb 744, 7 (2015). 120 Sn(γ,γ ): B. Özel-Tashenov, et al., PRC 90, (2014). Exp.&Theoretical predictions (2014) (2014) (2008) (2013) (2007)

18 FIRST SYSTEMATIC STUDIES OF THE PDR IN N=50 ISOTONES Proton number increasing, neutron skin decreasing N=50,82 isotones S. Volz et al., Nucl. Phys. A, 779 (2006) 1-20; D. Savran et al.,prl 100, (2008) ; R. Schwengner et al, Phys. Rev. C 78 (2008) ; R. Schwengner et al, Phys. Rev. C 87, (2013). Neutron number increasing, neutron skin increasing N. Tsoneva, H. Lenske, Ch. Stoyanov, Phys. Lett. B 586 (2004) 213 N. Tsoneva, H. Lenske, Phys. Rev. C 77 (2008) ; A. Tonchev et al., to be submitted. Z=50,82 chains Theoretical prediction of Pygmy Quadrupole Resonance N. Tsoneva, H. Lenske, Phys. Lett. B 695 (2011). Z=50 isotopes R. Schwengner et al., Phys. Rev. C 87, (2013)

19 DYNAMICS OF NUCLEAR EXCITATIONS IN N=50 ISOTONES exp: R. Schwengner et al., First systematic photon-scattering experiments in N=50 nuclei: using bremsstrahlung produced with electron beams at the linear accelerator ELBE, Rossendorf and quasi-monoenergetic γ rays at HIγS facility, Duke university. N. Tsoneva, S. Goriely, H. Lenske, R.Schwengner, PRC 91, (2015). R. Schwengner et al,prc87, (2013). N.Tsoneva, DPG15

20 Total cross section of 85 Kr g ( n,γ) 86 Kr reaction R. Raut et al., Phys. Rev. Lett. 111, (2013). A way to investigate 85 Kr branching point and the s-process: 85 Kr ( τ ~ Y) ground state is a branching point and thus a bridge for the production of 86 Kr at low neutron densities. R. Raut et al., PRL 111, (2013). R. Raut et al., PRL 111, (2013). R. Schwengner et al., PRC 87, (2013) (2013) S. Goriely

21 NEUTRON CAPTURE CROSS SECTIONS of the 85 Kr(n,γ) 86 Kr, 87 Sr(n,γ) 88 Sr, 89 Zr(n,γ) 90 Zr and 91 Mo(n,γ) 92 Mo reactions calculated with TALYS using EDF+QRPA, HFB+QRPA and three-phonon QPM strength functions. N. Tsoneva, S. Goriely, H. Lenske, R.Schwengner, PRC 91, (2015). ~ 50% increase ~ 22% increase ~ 13% increase ~ 10% increase For 85 Kr(n,γ) 86 Kr cross sections, the hashed area corresponds to the cross section determined with the experimental strength as derived in R. Raut et al., Phys. Rev. Lett. 111, (2013). For 87 Sr(n,γ) 88 Sr, TALYS cross sections are compared with experimental data G. Walter, Kernforschungszentrum Karlsruhe Reports No.3706 (1984); R.L. Macklin and J.H. Gibbons, Phys. Rev. 159, 1007 (1967).

22 Proton capture cross section of the 89 Y(p,γ) 90 Zr calculated with TALYS using EDF +QRPA, HFB+QRPA and three-phonon QPM strength functions. N. Tsoneva, S. Goriely, H. Lenske, R.Schwengner, PRC 91, (2015). < 10% increase

23 Maxwellian-averaged cross sections (in mb) at thermal energy of kt=30 KeV. N. Tsoneva, S. Goriely, H. Lenske, R.Schwengner, PRC 91, (2015). [5] R. Raut et al., PRL 111, (2013). [7] Z. Y. Bao et al., At. Data Nucl. Data Tables 76, 70 (2000).

24 OBSERVATION OF DOUBLE PYGMY RESONANCES IN 196 Pt preliminary

25 Conclusions A new theoretical method based on Density Functional Theory and Quasiparticle-Phonon Model is developed. Presently, this is the only existing method allowing for sufficiently large configuration space such that a unified description of low-energy single-particle, multiple-phonon states and the giant resonances is feasible. Different applications of the method are presented: - systematic studies of low energy dipole strengths reveal new mode of nuclear excitation - Pygmy Dipole Resonance as a unique mode of excitation correlated with the size of the neutron skin. - theoretical prediction of a higher order multipole pygmy resonance Pygmy Quadrupole Resonance. - studies of low-energy 0 + and multi-phonon states. - description of the fragmentation pattern of E1, E2 and M1 strengths - nuclear structure input for astrophysics